Principal Oscillation Patterns: A Review

Abstract

The principal oscillation pattern (POP) analysis is a technique used to simultaneously infer the characteristic patterns and timescales of a vector time series. The POPs may be seen as the normal modes of a linearized system whose system matrix is estimated from data. The concept of POP analysis is reviewed. Examples are used to illustrate the potential of the POP technique. The best defined POPs of tropospheric day-to-day variability coincide with the most unstable modes derived from linearized theory. POPs can be derived even from a space-time subset of data. POPs are successful in identifying two independent modes with similar timescales in the same dataset. The POP method can also produce forecasts that may potentially be used as a reference for other forecast models. The conventional POP analysis technique has been generalized in various ways. In the cyclostationary POP analysis, the estimated system matrix is allowed to vary deterministically with an externally forced cycle. In the complex POP analysis, not only the state of the system but also its ?momentum? is modeled. Associated correlation patterns are a useful tool to describe the appearance of a signal previously identified by a POP analysis in other parameters.